Accessories for rifles, such as rangefinders, infrared lasers, and other secondary sighting instruments, are commonly used as auxiliary instruments when a scope is already mounted to the weapon. Traditionally, these accessories are either attached directly to the scope tube or are attached to the scope mount by replacing the scope mount rings or ring caps with a ring or cap having a mountable feature (e.g., Picatinny rail). However, both of these traditional options have significant disadvantages. For instance, when attaching the accessory directly to a scope tube, unnecessary stress is placed on the scope tube, which can damage this delicate piece of equipment. And attaching the accessory to scope mount rings or caps requires the accessory to be cantilevered out over the objective lens of the scope, potentially obscuring the user's view. Also, when the weapon is fired, an accessory attached to scope mount rings or caps is vulnerable to significant vibration (similar to a diving board), which can hinder the accuracy of the accessory and its ability to stay on target. Further, handling the scope mount for the purpose of replacing a scope ring or cap will disrupt the mounting positioning of the scope itself, again potentially reducing the accuracy of the scope and requiring further adjustment. Accordingly, there is a need for an improved mounting system for auxiliary accessories.